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a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=191, a(1)=1587, a(2)=14161, a(3)=123004, a(4)=508152.
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%I #19 Jun 30 2023 15:29:04

%S 191,1587,14161,123004,508152,2064880,8324064,33425344,133959552,

%T 536354560,2146450944,8587869184,34355607552,137430691840,

%U 549739290624,2198990209024,8796026929152,35184239902720,140737223983104

%N a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=191, a(1)=1587, a(2)=14161, a(3)=123004, a(4)=508152.

%C Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+1)/6, i.e., one sixth of second quadrisection of A077076.

%H Vincenzo Librandi, <a href="/A177683/b177683.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -8).

%F a(n) = 2*4^(n+5)-2017*2^(n-1) for n > 2.

%F G.f.: (191+441*x+6167*x^2+50734*x^3-116584*x^4) / ((1-2*x)*(1-4*x)).

%F G.f. for the sequence starting at a(3): 4*x^3*(30751-57468*x) / ((1-2*x)*(1-4*x)).

%t Join[{191,1587,14161},Transpose[NestList[{Last[#],6Last[#]-8First[#]}&,{123004,508152},20]][[1]]] (* _Harvey P. Dale_, Mar 06 2011 *)

%t CoefficientList[Series[(191 + 441 x + 6167 x^2 + 50734 x^3 - 116584 x^4)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)

%t LinearRecurrence[{6,-8},{191,1587,14161,123004,508152},20] (* _Harvey P. Dale_, Oct 16 2019 *)

%o (PARI) {m=19; v=concat([191, 1587, 14161, 123004, 508152], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]); v}

%o (Magma) [191, 1587, 14161] cat [2*4^(n+5)-2017*2^(n-1): n in [3..25]]; // _Vincenzo Librandi_, Sep 24 2013

%Y Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177682, A177684, A177685.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, May 12 2010